LMFDB - Embedded newform 2592.2.r.q.2161.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2592,2,Mod(433,2592)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2592, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2592.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2592 = 2^{5} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2592.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.6972242039$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} + 2x^{12} + 12x^{10} - 28x^{8} + 48x^{6} + 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 + 2x^12 + 12x^10 - 28x^8 + 48x^6 + 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2161.8
Root			$1.04852 + 0.948998i$ of defining polynomial
Character	$\chi$	$=$	2592.2161
Dual form			2592.2.r.q.433.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.91009 - 1.68014i) q^{5} +(-1.32288 + 2.29129i) q^{7} +O(q^{10})$	$q+(2.91009 - 1.68014i) q^{5} +(-1.32288 + 2.29129i) q^{7} +(-1.87919 - 1.08495i) q^{11} +(4.02334 - 2.32288i) q^{13} -4.55066 q^{17} -6.29150i q^{19} +(-0.489766 - 0.848299i) q^{23} +(3.14575 - 5.44860i) q^{25} +(-3.75839 - 2.16991i) q^{29} +(1.00000 + 1.73205i) q^{31} +8.89047i q^{35} -1.35425i q^{37} +(-5.53019 - 9.57857i) q^{41} +(-2.85052 - 1.64575i) q^{43} +(5.04042 - 8.73027i) q^{47} +4.33981i q^{53} -7.29150 q^{55} +(9.76117 - 5.63561i) q^{59} +(1.67771 + 0.968627i) q^{61} +(7.80552 - 13.5196i) q^{65} +(2.59808 - 1.50000i) q^{67} +11.5830 q^{73} +(4.97188 - 2.87052i) q^{77} +(-4.32288 + 7.48744i) q^{79} +(2.06179 + 1.19038i) q^{83} +(-13.2428 + 7.64575i) q^{85} +4.55066 q^{89} +12.2915i q^{91} +(-10.5706 - 18.3088i) q^{95} +(-1.14575 + 1.98450i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 8 q^{25} + 16 q^{31} - 32 q^{55} + 16 q^{73} - 48 q^{79} + 24 q^{97}+O(q^{100}) $ 16 * q + 8 * q^25 + 16 * q^31 - 32 * q^55 + 16 * q^73 - 48 * q^79 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times$.

$n$	$325$	$1217$	$2431$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.91009	−	1.68014i	1.30143	−	0.751382i	0.320782	−	0.947153i	$-0.396054\pi$
$5$	2.91009	−	1.68014i	1.30143	−	0.751382i	0.980650	+	0.195771i	$0.0627209\pi$
$6$		0			0
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i	−1.00000			$\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.87919	−	1.08495i	−0.566599	−	0.327126i	0.189191	−	0.981940i	$-0.439413\pi$
$11$	−1.87919	−	1.08495i	−0.566599	−	0.327126i	−0.755790	+	0.654814i	$0.772747\pi$
$12$		0			0
$13$	4.02334	−	2.32288i	1.11587	−	0.644250i	0.175529	−	0.984474i	$-0.443836\pi$
$13$	4.02334	−	2.32288i	1.11587	−	0.644250i	0.940344	+	0.340224i	$0.110503\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.55066			−1.10370			−0.551848	−	0.833944i	$-0.686077\pi$
$17$	−4.55066			−1.10370			−0.551848	+	0.833944i	$0.686077\pi$
$18$		0			0
$19$		−	6.29150i		−	1.44337i	−0.692222	−	0.721685i	$-0.743368\pi$
$19$		−	6.29150i		−	1.44337i	0.692222	−	0.721685i	$-0.256632\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.489766	−	0.848299i	−0.102123	−	0.176883i	0.810436	−	0.585827i	$-0.199230\pi$
$23$	−0.489766	−	0.848299i	−0.102123	−	0.176883i	−0.912559	+	0.408945i	$0.865897\pi$
$24$		0			0
$25$	3.14575	−	5.44860i	0.629150	−	1.08972i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.75839	−	2.16991i	−0.697915	−	0.402942i	0.108655	−	0.994080i	$-0.465346\pi$
$29$	−3.75839	−	2.16991i	−0.697915	−	0.402942i	−0.806571	+	0.591138i	$0.798679\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			8.89047i			1.50276i
$36$		0			0
$37$		−	1.35425i		−	0.222637i	−0.993785	−	0.111319i	$-0.964493\pi$
$37$		−	1.35425i		−	0.222637i	0.993785	−	0.111319i	$-0.0355074\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.53019	−	9.57857i	−0.863671	−	1.49592i	−0.868361	−	0.495932i	$-0.834826\pi$
$41$	−5.53019	−	9.57857i	−0.863671	−	1.49592i	0.00469049	−	0.999989i	$-0.498507\pi$
$42$		0			0
$43$	−2.85052	−	1.64575i	−0.434701	−	0.250975i	0.266646	−	0.963794i	$-0.414084\pi$
$43$	−2.85052	−	1.64575i	−0.434701	−	0.250975i	−0.701347	+	0.712820i	$0.747418\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.04042	−	8.73027i	0.735222	−	1.27344i	−0.219405	−	0.975634i	$-0.570411\pi$
$47$	5.04042	−	8.73027i	0.735222	−	1.27344i	0.954626	−	0.297807i	$-0.0962552\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$		0			0
$53$			4.33981i			0.596119i	0.954547	+	0.298060i	$0.0963394\pi$
$53$			4.33981i			0.596119i	−0.954547	+	0.298060i	$0.903661\pi$
$54$		0			0
$55$	−7.29150			−0.983186
$56$		0			0
$57$		0			0
$58$		0			0
$59$	9.76117	−	5.63561i	1.27080	−	0.733694i	0.295658	−	0.955294i	$-0.404461\pi$
$59$	9.76117	−	5.63561i	1.27080	−	0.733694i	0.975138	+	0.221600i	$0.0711278\pi$
$60$		0			0
$61$	1.67771	+	0.968627i	0.214809	+	0.124020i	0.603544	−	0.797329i	$-0.293755\pi$
$61$	1.67771	+	0.968627i	0.214809	+	0.124020i	−0.388735	+	0.921349i	$0.627088\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.80552	−	13.5196i	0.968156	−	1.67689i
$66$		0			0
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	−0.332830	−	0.942987i	$-0.608004\pi$
$67$	2.59808	−	1.50000i	0.317406	−	0.183254i	0.650236	+	0.759733i	$0.274670\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	11.5830			1.35569			0.677844	−	0.735206i	$-0.262914\pi$
$73$	11.5830			1.35569			0.677844	+	0.735206i	$0.262914\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.97188	−	2.87052i	0.566599	−	0.327126i
$78$		0			0
$79$	−4.32288	+	7.48744i	−0.486362	+	0.842403i	−0.999877	−	0.0156774i	$-0.995010\pi$
$79$	−4.32288	+	7.48744i	−0.486362	+	0.842403i	0.513516	+	0.858080i	$0.328343\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.06179	+	1.19038i	0.226311	+	0.130661i	0.608869	−	0.793271i	$-0.291623\pi$
$83$	2.06179	+	1.19038i	0.226311	+	0.130661i	−0.382558	+	0.923931i	$0.624957\pi$
$84$		0			0
$85$	−13.2428	+	7.64575i	−1.43639	+	0.829298i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.55066			0.482369			0.241184	−	0.970479i	$-0.422464\pi$
$89$	4.55066			0.482369			0.241184	+	0.970479i	$0.422464\pi$
$90$		0			0
$91$			12.2915i			1.28850i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−10.5706	−	18.3088i	−1.08452	−	1.87845i
$96$		0			0
$97$	−1.14575	+	1.98450i	−0.116333	+	0.201495i	−0.918312	−	0.395857i	$-0.870447\pi$
$97$	−1.14575	+	1.98450i	−0.116333	+	0.201495i	0.801979	+	0.597353i	$0.203781\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.82018	+	3.36028i	0.579130	+	0.334361i	0.760787	−	0.649001i	$-0.224813\pi$
$101$	5.82018	+	3.36028i	0.579130	+	0.334361i	−0.181658	+	0.983362i	$0.558146\pi$
$102$		0			0
$103$	−2.67712	−	4.63692i	−0.263785	−	0.456889i	0.703460	−	0.710735i	$-0.251638\pi$
$103$	−2.67712	−	4.63692i	−0.263785	−	0.456889i	−0.967245	+	0.253846i	$0.918304\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	17.9918i		−	1.73933i	−0.493640	−	0.869666i	$-0.664334\pi$
$107$		−	17.9918i		−	1.73933i	0.493640	−	0.869666i	$-0.335666\pi$
$108$		0			0
$109$			15.2915i			1.46466i	0.680950	+	0.732330i	$0.261567\pi$
$109$			15.2915i			1.46466i	−0.680950	+	0.732330i	$0.738433\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.25486	−	5.63758i	−0.306192	−	0.530339i	0.671334	−	0.741155i	$-0.265721\pi$
$113$	−3.25486	−	5.63758i	−0.306192	−	0.530339i	−0.977526	+	0.210815i	$0.932388\pi$
$114$		0			0
$115$	−2.85052	−	1.64575i	−0.265813	−	0.153467i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.01996	−	10.4269i	0.551848	−	0.955830i
$120$		0			0
$121$	−3.14575	−	5.44860i	−0.285977	−	0.495327i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	4.33981i		−	0.388165i
$126$		0			0
$127$	−5.29150			−0.469545			−0.234772	−	0.972050i	$-0.575435\pi$
$127$	−5.29150			−0.469545			−0.234772	+	0.972050i	$0.575435\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−13.3370	+	7.70010i	−1.16526	+	0.672761i	−0.952558	−	0.304357i	$-0.901558\pi$
$131$	−13.3370	+	7.70010i	−1.16526	+	0.672761i	−0.212698	+	0.977118i	$0.568225\pi$
$132$		0			0
$133$	14.4156	+	8.32288i	1.24999	+	0.721685i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.25486	−	5.63758i	0.278082	−	0.481651i	−0.692826	−	0.721104i	$-0.743635\pi$
$137$	3.25486	−	5.63758i	0.278082	−	0.481651i	0.970908	+	0.239453i	$0.0769681\pi$
$138$		0			0
$139$	−10.6448	+	6.14575i	−0.902876	+	0.521276i	−0.878132	−	0.478418i	$-0.841210\pi$
$139$	−10.6448	+	6.14575i	−0.902876	+	0.521276i	−0.0247440	+	0.999694i	$0.507877\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−10.0808			−0.843003
$144$		0			0
$145$	−14.5830			−1.21105
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.51678	+	4.33981i	−0.615799	+	0.355531i	−0.775231	−	0.631677i	$-0.782367\pi$
$149$	−7.51678	+	4.33981i	−0.615799	+	0.355531i	0.159433	+	0.987209i	$0.449033\pi$
$150$		0			0
$151$	6.32288	−	10.9515i	0.514548	−	0.891224i	−0.485309	−	0.874343i	$-0.661293\pi$
$151$	6.32288	−	10.9515i	0.514548	−	0.891224i	0.999858	−	0.0168812i	$-0.00537372\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.82018	+	3.36028i	0.467488	+	0.269904i
$156$		0			0
$157$	7.54178	−	4.35425i	0.601900	−	0.347507i	−0.167889	−	0.985806i	$-0.553695\pi$
$157$	7.54178	−	4.35425i	0.601900	−	0.347507i	0.769789	+	0.638299i	$0.220362\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.59160			0.204246
$162$		0			0
$163$			6.29150i			0.492789i	0.969170	+	0.246394i	$0.0792458\pi$
$163$			6.29150i			0.492789i	−0.969170	+	0.246394i	$0.920754\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.59108	−	16.6122i	−0.742180	−	1.28549i	−0.951501	−	0.307647i	$-0.900458\pi$
$167$	−9.59108	−	16.6122i	−0.742180	−	1.28549i	0.209320	−	0.977847i	$-0.432875\pi$
$168$		0			0
$169$	4.29150	−	7.43310i	0.330116	−	0.571777i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	13.7022	+	7.91094i	1.04176	+	0.601458i	0.920330	−	0.391143i	$-0.127920\pi$
$173$	13.7022	+	7.91094i	1.04176	+	0.601458i	0.121425	+	0.992601i	$0.461253\pi$
$174$		0			0
$175$	8.32288	+	14.4156i	0.629150	+	1.08972i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			4.76150i			0.355891i	0.984040	+	0.177946i	$0.0569452\pi$
$179$			4.76150i			0.355891i	−0.984040	+	0.177946i	$0.943055\pi$
$180$		0			0
$181$		−	16.6458i		−	1.23727i	−0.785679	−	0.618634i	$-0.787686\pi$
$181$		−	16.6458i		−	1.23727i	0.785679	−	0.618634i	$-0.212314\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.27533	−	3.94099i	−0.167286	−	0.289747i
$186$		0			0
$187$	8.55157	+	4.93725i	0.625353	+	0.361048i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.06089	+	7.03367i	−0.293836	+	0.508939i	−0.974713	−	0.223459i	$-0.928265\pi$
$191$	−4.06089	+	7.03367i	−0.293836	+	0.508939i	0.680878	+	0.732397i	$0.261599\pi$
$192$		0			0
$193$	2.14575	+	3.71655i	0.154455	+	0.267523i	0.932860	−	0.360238i	$-0.117305\pi$
$193$	2.14575	+	3.71655i	0.154455	+	0.267523i	−0.778406	+	0.627762i	$0.783971\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	7.70010i		−	0.548609i	−0.961643	−	0.274305i	$-0.911552\pi$
$197$		−	7.70010i		−	0.548609i	0.961643	−	0.274305i	$-0.0884477\pi$
$198$		0			0
$199$	18.5203			1.31287			0.656433	−	0.754384i	$-0.272064\pi$
$199$	18.5203			1.31287			0.656433	+	0.754384i	$0.272064\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	9.94376	−	5.74103i	0.697915	−	0.402942i
$204$		0			0
$205$	−32.1867	−	18.5830i	−2.24802	−	1.29789i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.82599	+	11.8230i	−0.472163	+	0.817811i
$210$		0			0
$211$	0.252449	−	0.145751i	0.0173793	−	0.0100339i	−0.491285	−	0.870999i	$-0.663473\pi$
$211$	0.252449	−	0.145751i	0.0173793	−	0.0100339i	0.508664	+	0.860965i	$0.330139\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−11.0604			−0.754312
$216$		0			0
$217$	−5.29150			−0.359211
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−18.3088	+	10.5706i	−1.23159	+	0.711057i
$222$		0			0
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	−0.983451	−	0.181173i	$-0.942010\pi$
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	0.648626	+	0.761107i	$0.275344\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.6404	+	6.72057i	0.772598	+	0.446060i	0.833801	−	0.552066i	$-0.186160\pi$
$227$	11.6404	+	6.72057i	0.772598	+	0.446060i	−0.0612026	+	0.998125i	$0.519494\pi$
$228$		0			0
$229$	11.4021	−	6.58301i	0.753472	−	0.435017i	−0.0734751	−	0.997297i	$-0.523409\pi$
$229$	11.4021	−	6.58301i	0.753472	−	0.435017i	0.826947	+	0.562280i	$0.190076\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.10132			−0.596247			−0.298124	−	0.954527i	$-0.596361\pi$
$233$	−9.10132			−0.596247			−0.298124	+	0.954527i	$0.596361\pi$
$234$		0			0
$235$		−	33.8745i		−	2.20973i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	10.0808	+	17.4605i	0.652076	+	1.12943i	0.982618	+	0.185637i	$0.0594350\pi$
$239$	10.0808	+	17.4605i	0.652076	+	1.12943i	−0.330542	+	0.943791i	$0.607232\pi$
$240$		0			0
$241$	−13.4373	+	23.2740i	−0.865570	+	1.49921i	0.000910857		1.00000i	$0.499710\pi$
$241$	−13.4373	+	23.2740i	−0.865570	+	1.49921i	−0.866480	+	0.499211i	$0.833623\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−14.6144	−	25.3128i	−0.929891	−	1.61062i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	24.5015i		−	1.54652i	−0.634088	−	0.773261i	$-0.718624\pi$
$251$		−	24.5015i		−	1.54652i	0.634088	−	0.773261i	$-0.281376\pi$
$252$		0			0
$253$			2.12549i			0.133629i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.0808	−	17.4605i	−0.628826	−	1.08916i	−0.987788	−	0.155806i	$-0.950202\pi$
$257$	−10.0808	−	17.4605i	−0.628826	−	1.08916i	0.358962	−	0.933352i	$-0.383131\pi$
$258$		0			0
$259$	3.10297	+	1.79150i	0.192809	+	0.111319i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.979531	+	1.69660i	−0.0604005	+	0.104617i	−0.894644	−	0.446779i	$-0.852571\pi$
$263$	−0.979531	+	1.69660i	−0.0604005	+	0.104617i	0.834244	+	0.551395i	$0.185904\pi$
$264$		0			0
$265$	7.29150	+	12.6293i	0.447913	+	0.775809i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	5.74103i		−	0.350037i	−0.984565	−	0.175019i	$-0.944001\pi$
$269$		−	5.74103i		−	0.350037i	0.984565	−	0.175019i	$-0.0559985\pi$
$270$		0			0
$271$	21.2288			1.28956			0.644778	−	0.764370i	$-0.276950\pi$
$271$	21.2288			1.28956			0.644778	+	0.764370i	$0.276950\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−11.8230	+	6.82599i	−0.712951	+	0.411623i
$276$		0			0
$277$	7.54178	+	4.35425i	0.453142	+	0.261621i	0.709156	−	0.705052i	$-0.249076\pi$
$277$	7.54178	+	4.35425i	0.453142	+	0.261621i	−0.256014	+	0.966673i	$0.582409\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	10.0808	−	17.4605i	0.601373	−	1.04161i	−0.391240	−	0.920289i	$-0.627954\pi$
$281$	10.0808	−	17.4605i	0.601373	−	1.04161i	0.992613	−	0.121320i	$-0.0387128\pi$
$282$		0			0
$283$	23.6351	−	13.6458i	1.40496	−	0.811156i	0.410066	−	0.912056i	$-0.365506\pi$
$283$	23.6351	−	13.6458i	1.40496	−	0.811156i	0.994897	+	0.100900i	$0.0321722\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	29.2630			1.72734
$288$		0			0
$289$	3.70850			0.218147
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.4887	−	7.21033i	0.729595	−	0.421232i	−0.0886788	−	0.996060i	$-0.528264\pi$
$293$	12.4887	−	7.21033i	0.729595	−	0.421232i	0.818274	+	0.574828i	$0.194931\pi$
$294$		0			0
$295$	18.9373	−	32.8003i	1.10257	−	1.90971i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.94099	−	2.27533i	−0.227913	−	0.131586i
$300$		0			0
$301$	7.54178	−	4.35425i	0.434701	−	0.250975i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.50972			0.372746
$306$		0			0
$307$			9.87451i			0.563568i	0.959478	+	0.281784i	$0.0909261\pi$
$307$			9.87451i			0.563568i	−0.959478	+	0.281784i	$0.909074\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.489766	−	0.848299i	−0.0277721	−	0.0481026i	0.851805	−	0.523858i	$-0.175508\pi$
$311$	−0.489766	−	0.848299i	−0.0277721	−	0.0481026i	−0.879577	+	0.475756i	$0.842175\pi$
$312$		0			0
$313$	−7.43725	+	12.8817i	−0.420378	+	0.728117i	−0.995976	−	0.0896160i	$-0.971436\pi$
$313$	−7.43725	+	12.8817i	−0.420378	+	0.728117i	0.575598	+	0.817733i	$0.304769\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.8257	−	10.2917i	−1.00119	−	0.578039i	−0.0925920	−	0.995704i	$-0.529515\pi$
$317$	−17.8257	−	10.2917i	−1.00119	−	0.578039i	−0.908601	+	0.417665i	$0.862849\pi$
$318$		0			0
$319$	4.70850	+	8.15536i	0.263625	+	0.456612i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			28.6305i			1.59304i
$324$		0			0
$325$		−	29.2288i		−	1.62132i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	13.3357	+	23.0981i	0.735222	+	1.27344i
$330$		0			0
$331$	4.94370	+	2.85425i	0.271731	+	0.156884i	0.629674	−	0.776860i	$-0.283189\pi$
$331$	4.94370	+	2.85425i	0.271731	+	0.156884i	−0.357943	+	0.933743i	$0.616522\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.04042	−	8.73027i	0.275388	−	0.476986i
$336$		0			0
$337$	−1.14575	−	1.98450i	−0.0624131	−	0.108103i	0.833130	−	0.553076i	$-0.186546\pi$
$337$	−1.14575	−	1.98450i	−0.0624131	−	0.108103i	−0.895544	+	0.444974i	$0.853213\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	4.33981i		−	0.235014i
$342$		0			0
$343$	−18.5203			−1.00000
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.365193	+	0.210845i	−0.0196046	+	0.0113187i	−0.509770	−	0.860311i	$-0.670270\pi$
$347$	−0.365193	+	0.210845i	−0.0196046	+	0.0113187i	0.490166	+	0.871629i	$0.336936\pi$
$348$		0			0
$349$	−9.21949	−	5.32288i	−0.493508	−	0.284927i	0.232521	−	0.972591i	$-0.425303\pi$
$349$	−9.21949	−	5.32288i	−0.493508	−	0.284927i	−0.726029	+	0.687664i	$0.758636\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.50972	+	11.2752i	−0.346478	+	0.600117i	−0.985621	−	0.168971i	$-0.945956\pi$
$353$	−6.50972	+	11.2752i	−0.346478	+	0.600117i	0.639144	+	0.769087i	$0.279289\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	21.1412			1.11579			0.557896	−	0.829911i	$-0.311609\pi$
$359$	21.1412			1.11579			0.557896	+	0.829911i	$0.311609\pi$
$360$		0			0
$361$	−20.5830			−1.08332
$362$		0			0
$363$		0			0
$364$		0			0
$365$	33.7076	−	19.4611i	1.76434	−	1.01864i
$366$		0			0
$367$	2.26013	−	3.91466i	0.117978	−	0.204344i	−0.800988	−	0.598680i	$-0.795692\pi$
$367$	2.26013	−	3.91466i	0.117978	−	0.204344i	0.918966	+	0.394336i	$0.129025\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.94376	−	5.74103i	−0.516255	−	0.298060i
$372$		0			0
$373$	−33.3595	+	19.2601i	−1.72729	+	0.997252i	−0.826601	+	0.562788i	$0.809729\pi$
$373$	−33.3595	+	19.2601i	−1.72729	+	0.997252i	−0.900689	+	0.434464i	$0.856938\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−20.1617			−1.03838
$378$		0			0
$379$			21.5830i			1.10864i	0.832302	+	0.554322i	$0.187022\pi$
$379$			21.5830i			1.10864i	−0.832302	+	0.554322i	$0.812978\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.0808	+	17.4605i	0.515107	+	0.892192i	0.999846	+	0.0175332i	$0.00558128\pi$
$383$	10.0808	+	17.4605i	0.515107	+	0.892192i	−0.484739	+	0.874659i	$0.661085\pi$
$384$		0			0
$385$	9.64575	−	16.7069i	0.491593	−	0.851464i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.60669	−	2.65967i	−0.233568	−	0.134851i	0.378649	−	0.925540i	$-0.376389\pi$
$389$	−4.60669	−	2.65967i	−0.233568	−	0.134851i	−0.612217	+	0.790690i	$0.709722\pi$
$390$		0			0
$391$	2.22876	+	3.86032i	0.112713	+	0.195225i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			29.0522i			1.46177i
$396$		0			0
$397$			15.2915i			0.767459i	0.923446	+	0.383729i	$0.125360\pi$
$397$			15.2915i			0.767459i	−0.923446	+	0.383729i	$0.874640\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.50972	+	11.2752i	0.325080	+	0.563055i	0.981529	−	0.191316i	$-0.0612754\pi$
$401$	6.50972	+	11.2752i	0.325080	+	0.563055i	−0.656449	+	0.754371i	$0.727942\pi$
$402$		0			0
$403$	8.04668	+	4.64575i	0.400834	+	0.231421i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.46930	+	2.54490i	−0.0728303	+	0.126146i
$408$		0			0
$409$	−4.14575	−	7.18065i	−0.204994	−	0.355060i	0.745137	−	0.666912i	$-0.232384\pi$
$409$	−4.14575	−	7.18065i	−0.204994	−	0.355060i	−0.950131	+	0.311851i	$0.899051\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			29.8209i			1.46739i
$414$		0			0
$415$	8.00000			0.392705
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.87919	−	1.08495i	0.0918047	−	0.0530035i	−0.453395	−	0.891310i	$-0.649787\pi$
$419$	1.87919	−	1.08495i	0.0918047	−	0.0530035i	0.545200	+	0.838306i	$0.316454\pi$
$420$		0			0
$421$	19.6118	+	11.3229i	0.955820	+	0.551843i	0.894884	−	0.446298i	$-0.147258\pi$
$421$	19.6118	+	11.3229i	0.955820	+	0.551843i	0.0609363	+	0.998142i	$0.480591\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−14.3152	+	24.7947i	−0.694391	+	1.20272i
$426$		0			0
$427$	−4.43881	+	2.56275i	−0.214809	+	0.124020i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−30.2425			−1.45673			−0.728366	−	0.685188i	$-0.759720\pi$
$431$	−30.2425			−1.45673			−0.728366	+	0.685188i	$0.759720\pi$
$432$		0			0
$433$	−0.125492			−0.00603077			−0.00301538	−	0.999995i	$-0.500960\pi$
$433$	−0.125492			−0.00603077			−0.00301538	+	0.999995i	$0.500960\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.33708	+	3.08136i	−0.255307	+	0.147402i
$438$		0			0
$439$	−5.58301	+	9.67005i	−0.266462	+	0.461526i	−0.967946	−	0.251160i	$-0.919188\pi$
$439$	−5.58301	+	9.67005i	−0.266462	+	0.461526i	0.701483	+	0.712686i	$0.252521\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−24.9773	−	14.4207i	−1.18671	−	0.685146i	−0.229152	−	0.973391i	$-0.573595\pi$
$443$	−24.9773	−	14.4207i	−1.18671	−	0.685146i	−0.957557	+	0.288244i	$0.906928\pi$
$444$		0			0
$445$	13.2428	−	7.64575i	0.627770	−	0.362443i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	19.5292			0.921638			0.460819	−	0.887494i	$-0.347556\pi$
$449$	19.5292			0.921638			0.460819	+	0.887494i	$0.347556\pi$
$450$		0			0
$451$			24.0000i			1.13012i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	20.6515	+	35.7694i	0.968156	+	1.67689i
$456$		0			0
$457$	−11.9373	+	20.6759i	−0.558401	+	0.967179i	0.439229	+	0.898375i	$0.355252\pi$
$457$	−11.9373	+	20.6759i	−0.558401	+	0.967179i	−0.997630	+	0.0688041i	$0.978082\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	16.2471	+	9.38024i	0.756701	+	0.436881i	0.828110	−	0.560566i	$-0.189416\pi$
$461$	16.2471	+	9.38024i	0.756701	+	0.436881i	−0.0714093	+	0.997447i	$0.522750\pi$
$462$		0			0
$463$	15.6144	+	27.0449i	0.725662	+	1.25688i	0.958701	+	0.284416i	$0.0917996\pi$
$463$	15.6144	+	27.0449i	0.725662	+	1.25688i	−0.233039	+	0.972467i	$0.574867\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			0.210845i			0.00975672i	0.999988	+	0.00487836i	$0.00155284\pi$
$467$			0.210845i			0.00975672i	−0.999988	+	0.00487836i	$0.998447\pi$
$468$		0			0
$469$			7.93725i			0.366508i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.57113	+	6.18537i	0.164201	+	0.284404i
$474$		0			0
$475$	−34.2799	−	19.7915i	−1.57287	−	0.908096i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.5701	+	30.4323i	−0.802798	+	1.39049i	0.114969	+	0.993369i	$0.463323\pi$
$479$	−17.5701	+	30.4323i	−0.802798	+	1.39049i	−0.917767	+	0.397119i	$0.870010\pi$
$480$		0			0
$481$	−3.14575	−	5.44860i	−0.143434	−	0.248435i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			7.70010i			0.349643i
$486$		0			0
$487$	−6.06275			−0.274729			−0.137365	−	0.990521i	$-0.543863\pi$
$487$	−6.06275			−0.274729			−0.137365	+	0.990521i	$0.543863\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.57579	−	2.06448i	0.161373	−	0.0931689i	−0.417139	−	0.908843i	$-0.636967\pi$
$491$	3.57579	−	2.06448i	0.161373	−	0.0931689i	0.578512	+	0.815674i	$0.303634\pi$
$492$		0			0
$493$	17.1031	+	9.87451i	0.770287	+	0.444725i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−37.8878	+	21.8745i	−1.69609	+	0.979237i	−0.746686	+	0.665176i	$0.768356\pi$
$499$	−37.8878	+	21.8745i	−1.69609	+	0.979237i	−0.949403	+	0.314061i	$0.898310\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2.93859			0.131025			0.0655127	−	0.997852i	$-0.479132\pi$
$503$	2.93859			0.131025			0.0655127	+	0.997852i	$0.479132\pi$
$504$		0			0
$505$	22.5830			1.00493
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−28.6178	+	16.5225i	−1.26846	+	0.732347i	−0.974697	−	0.223531i	$-0.928242\pi$
$509$	−28.6178	+	16.5225i	−1.26846	+	0.732347i	−0.293765	+	0.955878i	$0.594908\pi$
$510$		0			0
$511$	−15.3229	+	26.5400i	−0.677844	+	1.17406i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−15.5813	−	8.99590i	−0.686596	−	0.396407i
$516$		0			0
$517$	−18.9439	+	10.9373i	−0.833151	+	0.481020i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.6520			0.598104			0.299052	−	0.954237i	$-0.403330\pi$
$521$	13.6520			0.598104			0.299052	+	0.954237i	$0.403330\pi$
$522$		0			0
$523$			0.874508i			0.0382396i	0.999817	+	0.0191198i	$0.00608639\pi$
$523$			0.874508i			0.0382396i	−0.999817	+	0.0191198i	$0.993914\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.55066	−	7.88197i	−0.198230	−	0.343344i
$528$		0			0
$529$	11.0203	−	19.0876i	0.479142	−	0.829898i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−44.4997	−	25.6919i	−1.92749	−	1.11284i
$534$		0			0
$535$	−30.2288	−	52.3577i	−1.30690	−	2.26362i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$			26.5203i			1.14019i	0.821577	+	0.570097i	$0.193095\pi$
$541$			26.5203i			1.14019i	−0.821577	+	0.570097i	$0.806905\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	25.6919	+	44.4997i	1.10052	+	1.90616i
$546$		0			0
$547$	−8.29913	−	4.79150i	−0.354845	−	0.204870i	0.311972	−	0.950091i	$-0.399010\pi$
$547$	−8.29913	−	4.79150i	−0.354845	−	0.204870i	−0.666817	+	0.745221i	$0.732344\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13.6520	+	23.6459i	−0.581594	+	1.00735i
$552$		0			0
$553$	−11.4373	−	19.8099i	−0.486362	−	0.842403i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			1.40122i			0.0593716i	0.999559	+	0.0296858i	$0.00945067\pi$
$557$			1.40122i			0.0593716i	−0.999559	+	0.0296858i	$0.990549\pi$
$558$		0			0
$559$	−15.2915			−0.646762
$560$		0			0
$561$		0			0
$562$		0			0
$563$	36.2525	−	20.9304i	1.52786	−	0.882111i	0.528409	−	0.848990i	$-0.322789\pi$
$563$	36.2525	−	20.9304i	1.52786	−	0.882111i	0.999451	−	0.0331206i	$-0.0105445\pi$
$564$		0			0
$565$	−18.9439	−	10.9373i	−0.796975	−	0.460134i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.3357	+	23.0981i	−0.559062	+	0.968324i	0.438513	+	0.898725i	$0.355505\pi$
$569$	−13.3357	+	23.0981i	−0.559062	+	0.968324i	−0.997575	+	0.0695990i	$0.977828\pi$
$570$		0			0
$571$	4.94370	−	2.85425i	0.206888	−	0.119447i	−0.392977	−	0.919549i	$-0.628555\pi$
$571$	4.94370	−	2.85425i	0.206888	−	0.119447i	0.599864	+	0.800102i	$0.295221\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6.16272			−0.257003
$576$		0			0
$577$	23.5830			0.981773			0.490887	−	0.871223i	$-0.336673\pi$
$577$	23.5830			0.981773			0.490887	+	0.871223i	$0.336673\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.45499	+	3.14944i	−0.226311	+	0.130661i
$582$		0			0
$583$	4.70850	−	8.15536i	0.195006	−	0.337760i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	18.9745	+	10.9550i	0.783163	+	0.452160i	0.837550	−	0.546360i	$-0.183987\pi$
$587$	18.9745	+	10.9550i	0.783163	+	0.452160i	−0.0543869	+	0.998520i	$0.517320\pi$
$588$		0			0
$589$	10.8972	−	6.29150i	0.449011	−	0.259237i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−33.1811			−1.36259			−0.681293	−	0.732011i	$-0.738582\pi$
$593$	−33.1811			−1.36259			−0.681293	+	0.732011i	$0.738582\pi$
$594$		0			0
$595$		−	40.4575i		−	1.65860i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.5701	+	30.4323i	0.717895	+	1.24343i	0.961832	+	0.273639i	$0.0882275\pi$
$599$	17.5701	+	30.4323i	0.717895	+	1.24343i	−0.243937	+	0.969791i	$0.578439\pi$
$600$		0			0
$601$	15.9373	−	27.6041i	0.650094	−	1.12600i	−0.333006	−	0.942925i	$-0.608063\pi$
$601$	15.9373	−	27.6041i	0.650094	−	1.12600i	0.983100	−	0.183071i	$-0.0586039\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−18.3088	−	10.5706i	−0.744360	−	0.429757i
$606$		0			0
$607$	16.6771	+	28.8856i	0.676904	+	1.17243i	0.975909	+	0.218180i	$0.0700119\pi$
$607$	16.6771	+	28.8856i	0.676904	+	1.17243i	−0.299005	+	0.954252i	$0.596655\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	46.8331i		−	1.89467i
$612$		0			0
$613$			21.1033i			0.852353i	0.904640	+	0.426176i	$0.140140\pi$
$613$			21.1033i			0.852353i	−0.904640	+	0.426176i	$0.859860\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.78505	+	15.2162i	0.353673	+	0.612579i	0.986890	−	0.161395i	$-0.0515993\pi$
$617$	8.78505	+	15.2162i	0.353673	+	0.612579i	−0.633217	+	0.773974i	$0.718266\pi$
$618$		0			0
$619$	33.7750	+	19.5000i	1.35753	+	0.783771i	0.989291	−	0.145959i	$-0.0466268\pi$
$619$	33.7750	+	19.5000i	1.35753	+	0.783771i	0.368241	+	0.929730i	$0.379960\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.01996	+	10.4269i	−0.241184	+	0.417744i
$624$		0			0
$625$	8.43725	+	14.6138i	0.337490	+	0.584550i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			6.16272i			0.245724i
$630$		0			0
$631$	−19.2288			−0.765485			−0.382742	−	0.923855i	$-0.625020\pi$
$631$	−19.2288			−0.765485			−0.382742	+	0.923855i	$0.625020\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−15.3988	+	8.89047i	−0.611081	+	0.352808i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−11.0604	+	19.1571i	−0.436859	+	0.756662i	−0.997445	−	0.0714343i	$-0.977242\pi$
$641$	−11.0604	+	19.1571i	−0.436859	+	0.756662i	0.560587	+	0.828096i	$0.310576\pi$
$642$		0			0
$643$	23.6351	−	13.6458i	0.932079	−	0.538136i	0.0446103	−	0.999004i	$-0.485795\pi$
$643$	23.6351	−	13.6458i	0.932079	−	0.538136i	0.887468	+	0.460869i	$0.152462\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−33.1811			−1.30449			−0.652243	−	0.758010i	$-0.726172\pi$
$647$	−33.1811			−1.30449			−0.652243	+	0.758010i	$0.726172\pi$
$648$		0			0
$649$	−24.4575			−0.960041
$650$		0			0
$651$		0			0
$652$		0			0
$653$	21.2189	−	12.2508i	0.830361	−	0.479409i	−0.0236153	−	0.999721i	$-0.507518\pi$
$653$	21.2189	−	12.2508i	0.830361	−	0.479409i	0.853976	+	0.520312i	$0.174184\pi$
$654$		0			0
$655$	−25.8745	+	44.8160i	−1.01100	+	1.75110i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.94376	+	5.74103i	0.387354	+	0.223639i	0.681013	−	0.732271i	$-0.261540\pi$
$659$	9.94376	+	5.74103i	0.387354	+	0.223639i	−0.293659	+	0.955910i	$0.594873\pi$
$660$		0			0
$661$	12.5749	−	7.26013i	0.489107	−	0.282386i	−0.235097	−	0.971972i	$-0.575541\pi$
$661$	12.5749	−	7.26013i	0.489107	−	0.282386i	0.724204	+	0.689586i	$0.242207\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	55.9344			2.16904
$666$		0			0
$667$			4.25098i			0.164599i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.10183	−	3.64048i	−0.0811403	−	0.140539i
$672$		0			0
$673$	20.4373	−	35.3984i	0.787798	−	1.36451i	−0.139515	−	0.990220i	$-0.544554\pi$
$673$	20.4373	−	35.3984i	0.787798	−	1.36451i	0.927313	−	0.374287i	$-0.122112\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	27.5222	+	15.8900i	1.05776	+	0.610701i	0.924813	−	0.380422i	$-0.124221\pi$
$677$	27.5222	+	15.8900i	1.05776	+	0.610701i	0.132952	+	0.991123i	$0.457554\pi$
$678$		0			0
$679$	−3.03137	−	5.25049i	−0.116333	−	0.201495i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			17.7809i			0.680369i	0.940359	+	0.340185i	$0.110490\pi$
$683$			17.7809i			0.680369i	−0.940359	+	0.340185i	$0.889510\pi$
$684$		0			0
$685$		−	21.8745i		−	0.835782i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	10.0808	+	17.4605i	0.384050	+	0.665194i
$690$		0			0
$691$	23.6351	+	13.6458i	0.899123	+	0.519109i	0.876916	−	0.480645i	$-0.159597\pi$
$691$	23.6351	+	13.6458i	0.899123	+	0.519109i	0.0222074	+	0.999753i	$0.492931\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−20.6515	+	35.7694i	−0.783355	+	1.35681i
$696$		0			0
$697$	25.1660	+	43.5888i	0.953231	+	1.65104i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	16.8014i		−	0.634581i	−0.948328	−	0.317290i	$-0.897227\pi$
$701$		−	16.8014i		−	0.634581i	0.948328	−	0.317290i	$-0.102773\pi$
$702$		0			0
$703$	−8.52026			−0.321348
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.3988	+	8.89047i	−0.579130	+	0.334361i
$708$		0			0
$709$	−3.01354	−	1.73987i	−0.113176	−	0.0653422i	0.442343	−	0.896846i	$-0.354147\pi$
$709$	−3.01354	−	1.73987i	−0.113176	−	0.0653422i	−0.555519	+	0.831504i	$0.687481\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.979531	−	1.69660i	0.0366837	−	0.0635381i
$714$		0			0
$715$	−29.3362	+	16.9373i	−1.09711	+	0.633417i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	51.3838			1.91629			0.958146	−	0.286281i	$-0.0924190\pi$
$719$	51.3838			1.91629			0.958146	+	0.286281i	$0.0924190\pi$
$720$		0			0
$721$	14.1660			0.527570
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−23.6459	+	13.6520i	−0.878187	+	0.507022i
$726$		0			0
$727$	22.2915	−	38.6100i	0.826746	−	1.43197i	−0.0738314	−	0.997271i	$-0.523523\pi$
$727$	22.2915	−	38.6100i	0.826746	−	1.43197i	0.900578	−	0.434695i	$-0.143144\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12.9718	+	7.48925i	0.479778	+	0.277000i
$732$		0			0
$733$	24.6449	−	14.2288i	0.910281	−	0.525551i	0.0297596	−	0.999557i	$-0.490526\pi$
$733$	24.6449	−	14.2288i	0.910281	−	0.525551i	0.880522	+	0.474006i	$0.157192\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.50972			−0.239789
$738$		0			0
$739$		−	40.4575i		−	1.48825i	−0.668038	−	0.744127i	$-0.732866\pi$
$739$		−	40.4575i		−	1.48825i	0.668038	−	0.744127i	$-0.267134\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.5297	−	21.7020i	−0.459669	−	0.796171i	0.539274	−	0.842130i	$-0.318699\pi$
$743$	−12.5297	−	21.7020i	−0.459669	−	0.796171i	−0.998943	+	0.0459598i	$0.985365\pi$
$744$		0			0
$745$	−14.5830	+	25.2585i	−0.534280	+	0.925400i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	41.2244	+	23.8009i	1.50631	+	0.869666i
$750$		0			0
$751$	12.0314	+	20.8389i	0.439031	+	0.760424i	0.997615	−	0.0690239i	$-0.0219885\pi$
$751$	12.0314	+	20.8389i	0.439031	+	0.760424i	−0.558584	+	0.829448i	$0.688655\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	42.4933i		−	1.54649i
$756$		0			0
$757$		−	13.9373i		−	0.506558i	−0.967393	−	0.253279i	$-0.918491\pi$
$757$		−	13.9373i		−	0.506558i	0.967393	−	0.253279i	$-0.0815091\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−4.86693	−	8.42976i	−0.176426	−	0.305579i	0.764228	−	0.644946i	$-0.223120\pi$
$761$	−4.86693	−	8.42976i	−0.176426	−	0.305579i	−0.940654	+	0.339368i	$0.889787\pi$
$762$		0			0
$763$	−35.0372	−	20.2288i	−1.26843	−	0.732330i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	26.1817	−	45.3480i	0.945365	−	1.63742i
$768$		0			0
$769$	−18.0830	−	31.3207i	−0.652090	−	1.12945i	−0.982615	−	0.185656i	$-0.940559\pi$
$769$	−18.0830	−	31.3207i	−0.652090	−	1.12945i	0.330525	−	0.943797i	$-0.392774\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			6.29888i			0.226555i	0.993563	+	0.113277i	$0.0361349\pi$
$773$			6.29888i			0.226555i	−0.993563	+	0.113277i	$0.963865\pi$
$774$		0			0
$775$	12.5830			0.451995
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−60.2636	+	34.7932i	−2.15917	+	1.24660i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.6315	−	25.3425i	0.522221	−	0.904513i
$786$		0			0
$787$	43.8413	−	25.3118i	1.56277	−	0.902267i	0.565797	−	0.824545i	$-0.308569\pi$
$787$	43.8413	−	25.3118i	1.56277	−	0.902267i	0.996975	−	0.0777223i	$-0.0247648\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	17.2231			0.612383
$792$		0			0
$793$	9.00000			0.319599
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−44.1345	+	25.4810i	−1.56332	+	0.902585i	−0.566406	+	0.824127i	$0.691666\pi$
$797$	−44.1345	+	25.4810i	−1.56332	+	0.902585i	−0.996917	+	0.0784582i	$0.975000\pi$
$798$		0			0
$799$	−22.9373	+	39.7285i	−0.811462	+	1.40549i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−21.7667	−	12.5670i	−0.768131	−	0.443481i
$804$		0			0
$805$	7.54178	−	4.35425i	0.265813	−	0.153467i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0			−	1.00000i	$-0.5\pi$
$809$		0			0				1.00000i	$0.5\pi$
$810$		0			0
$811$		−	20.7085i		−	0.727174i	−0.931560	−	0.363587i	$-0.881552\pi$
$811$		−	20.7085i		−	0.727174i	0.931560	−	0.363587i	$-0.118448\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.5706	+	18.3088i	0.370272	+	0.641331i
$816$		0			0
$817$	−10.3542	+	17.9341i	−0.362249	+	0.627434i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	43.2862	+	24.9913i	1.51070	+	0.872202i	0.999922	+	0.0124875i	$0.00397501\pi$
$821$	43.2862	+	24.9913i	1.51070	+	0.872202i	0.510776	+	0.859714i	$0.329358\pi$
$822$		0			0
$823$	−10.0314	−	17.3748i	−0.349672	−	0.605649i	0.636519	−	0.771261i	$-0.280374\pi$
$823$	−10.0314	−	17.3748i	−0.349672	−	0.605649i	−0.986191	+	0.165612i	$0.947040\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			49.6356i			1.72600i	0.505206	+	0.862999i	$0.331417\pi$
$827$			49.6356i			1.72600i	−0.505206	+	0.862999i	$0.668583\pi$
$828$		0			0
$829$		−	6.77124i		−	0.235175i	−0.993063	−	0.117588i	$-0.962484\pi$
$829$		−	6.77124i		−	0.235175i	0.993063	−	0.117588i	$-0.0375161\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−55.8218	−	32.2288i	−1.93179	−	1.11532i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.6110	−	27.0391i	0.538953	−	0.933494i	−0.460008	−	0.887915i	$-0.652153\pi$
$839$	15.6110	−	27.0391i	0.538953	−	0.933494i	0.998961	−	0.0455790i	$-0.0145133\pi$
$840$		0			0
$841$	−5.08301	−	8.80402i	−0.175276	−	0.303587i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	28.8413i		−	0.992172i
$846$		0			0
$847$	16.6458			0.571955
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.14881	+	0.663265i	−0.0393806	+	0.0227364i
$852$		0			0
$853$	25.8177	+	14.9059i	0.883983	+	0.510368i	0.871970	−	0.489560i	$-0.162843\pi$
$853$	25.8177	+	14.9059i	0.883983	+	0.510368i	0.0120132	+	0.999928i	$0.496176\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−20.1617	+	34.9211i	−0.688711	+	1.19288i	0.283545	+	0.958959i	$0.408490\pi$
$857$	−20.1617	+	34.9211i	−0.688711	+	1.19288i	−0.972255	+	0.233923i	$0.924844\pi$
$858$		0			0
$859$	22.8778	−	13.2085i	0.780580	−	0.450668i	−0.0560558	−	0.998428i	$-0.517852\pi$
$859$	22.8778	−	13.2085i	0.780580	−	0.450668i	0.836636	+	0.547760i	$0.184519\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−36.1197			−1.22953			−0.614765	−	0.788710i	$-0.710749\pi$
$863$	−36.1197			−1.22953			−0.614765	+	0.788710i	$0.710749\pi$
$864$		0			0
$865$	53.1660			1.80770
$866$		0			0
$867$		0			0
$868$		0			0
$869$	16.2471	−	9.38024i	0.551143	−	0.318203i
$870$		0			0
$871$	6.96863	−	12.0700i	0.236123	−	0.408977i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	9.94376	+	5.74103i	0.336161	+	0.194082i
$876$		0			0
$877$	−41.9111	+	24.1974i	−1.41524	+	0.817088i	−0.995875	−	0.0907316i	$-0.971079\pi$
$877$	−41.9111	+	24.1974i	−1.41524	+	0.817088i	−0.419362	+	0.907819i	$0.637746\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	31.8546			1.07321			0.536605	−	0.843834i	$-0.319707\pi$
$881$	31.8546			1.07321			0.536605	+	0.843834i	$0.319707\pi$
$882$		0			0
$883$			16.1660i			0.544030i	0.962293	+	0.272015i	$0.0876900\pi$
$883$			16.1660i			0.544030i	−0.962293	+	0.272015i	$0.912310\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.57113	−	6.18537i	−0.119907	−	0.207685i	0.799824	−	0.600235i	$-0.204926\pi$
$887$	−3.57113	−	6.18537i	−0.119907	−	0.207685i	−0.919731	+	0.392550i	$0.871593\pi$
$888$		0			0
$889$	7.00000	−	12.1244i	0.234772	−	0.406638i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−54.9265	−	31.7118i	−1.83805	−	1.06120i
$894$		0			0
$895$	8.00000	+	13.8564i	0.267411	+	0.463169i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	8.67963i		−	0.289482i
$900$		0			0
$901$		−	19.7490i		−	0.657935i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−27.9672	−	48.4406i	−0.929662	−	1.61022i
$906$		0			0
$907$	48.5325	+	28.0203i	1.61150	+	0.930397i	0.989024	+	0.147755i	$0.0472047\pi$
$907$	48.5325	+	28.0203i	1.61150	+	0.930397i	0.622472	+	0.782642i	$0.286129\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.7328	+	41.1065i	−0.786304	+	1.36192i	0.141914	+	0.989879i	$0.454674\pi$
$911$	−23.7328	+	41.1065i	−0.786304	+	1.36192i	−0.928217	+	0.372039i	$0.878659\pi$
$912$		0			0
$913$	−2.58301	−	4.47390i	−0.0854850	−	0.148064i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	40.7451i		−	1.34552i
$918$		0			0
$919$	−20.5830			−0.678971			−0.339485	−	0.940611i	$-0.610253\pi$
$919$	−20.5830			−0.678971			−0.339485	+	0.940611i	$0.610253\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−7.37876	−	4.26013i	−0.242612	−	0.140072i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	8.46878	−	14.6684i	0.277852	−	0.481253i	−0.692999	−	0.720939i	$-0.743711\pi$
$929$	8.46878	−	14.6684i	0.277852	−	0.481253i	0.970851	+	0.239685i	$0.0770442\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	33.1811			1.08514
$936$		0			0
$937$	−9.12549			−0.298117			−0.149058	−	0.988828i	$-0.547624\pi$
$937$	−9.12549			−0.298117			−0.149058	+	0.988828i	$0.547624\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.6740	−	10.7815i	0.608756	−	0.351466i	−0.163722	−	0.986506i	$-0.552350\pi$
$941$	18.6740	−	10.7815i	0.608756	−	0.351466i	0.772478	+	0.635041i	$0.219017\pi$
$942$		0			0
$943$	−5.41699	+	9.38251i	−0.176402	+	0.305537i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.8565	+	15.5056i	0.872720	+	0.503865i	0.868251	−	0.496125i	$-0.165244\pi$
$947$	26.8565	+	15.5056i	0.872720	+	0.503865i	0.00446852	+	0.999990i	$0.498578\pi$
$948$		0			0
$949$	46.6024	−	26.9059i	1.51278	−	0.873402i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−40.9559			−1.32669			−0.663346	−	0.748312i	$-0.730864\pi$
$953$	−40.9559			−1.32669			−0.663346	+	0.748312i	$0.730864\pi$
$954$		0			0
$955$			27.2915i			0.883132i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	8.61155	+	14.9156i	0.278082	+	0.481651i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	12.4887	+	7.21033i	0.402024	+	0.232109i
$966$		0			0
$967$	−19.0314	−	32.9633i	−0.612008	−	1.06003i	−0.990902	−	0.134588i	$-0.957029\pi$
$967$	−19.0314	−	32.9633i	−0.612008	−	1.06003i	0.378894	−	0.925440i	$-0.376305\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	17.9918i		−	0.577384i	−0.957422	−	0.288692i	$-0.906780\pi$
$971$		−	17.9918i		−	0.577384i	0.957422	−	0.288692i	$-0.0932204\pi$
$972$		0			0
$973$		−	32.5203i		−	1.04255i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−14.6315	−	25.3425i	−0.468103	−	0.810779i	0.531232	−	0.847226i	$-0.321729\pi$
$977$	−14.6315	−	25.3425i	−0.468103	−	0.810779i	−0.999336	+	0.0364474i	$0.988396\pi$
$978$		0			0
$979$	−8.55157	−	4.93725i	−0.273310	−	0.157795i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	14.1417	−	24.4942i	0.451052	−	0.781244i	−0.547400	−	0.836871i	$-0.684382\pi$
$983$	14.1417	−	24.4942i	0.451052	−	0.781244i	0.998452	+	0.0556269i	$0.0177157\pi$
$984$		0			0
$985$	−12.9373	−	22.4080i	−0.412215	−	0.713978i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			3.22413i			0.102521i
$990$		0			0
$991$	−21.9373			−0.696860			−0.348430	−	0.937335i	$-0.613285\pi$
$991$	−21.9373			−0.696860			−0.348430	+	0.937335i	$0.613285\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	53.8956	−	31.1167i	1.70861	−	0.986464i
$996$		0			0
$997$	−18.9439	−	10.9373i	−0.599959	−	0.346386i	0.169067	−	0.985605i	$-0.445925\pi$
$997$	−18.9439	−	10.9373i	−0.599959	−	0.346386i	−0.769025	+	0.639218i	$0.779258\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2592.2.r.q.2161.8		16
3.2	odd	2	inner	2592.2.r.q.2161.2		16
4.3	odd	2		648.2.n.q.541.5		16
8.3	odd	2		648.2.n.q.541.7		16
8.5	even	2	inner	2592.2.r.q.2161.1		16
9.2	odd	6		864.2.d.c.433.2		8
9.4	even	3	inner	2592.2.r.q.433.1		16
9.5	odd	6	inner	2592.2.r.q.433.7		16
9.7	even	3		864.2.d.c.433.8		8
12.11	even	2		648.2.n.q.541.4		16
24.5	odd	2	inner	2592.2.r.q.2161.7		16
24.11	even	2		648.2.n.q.541.2		16
36.7	odd	6		216.2.d.c.109.2	yes	8
36.11	even	6		216.2.d.c.109.7	yes	8
36.23	even	6		648.2.n.q.109.2		16
36.31	odd	6		648.2.n.q.109.7		16
72.5	odd	6	inner	2592.2.r.q.433.2		16
72.11	even	6		216.2.d.c.109.8	yes	8
72.13	even	6	inner	2592.2.r.q.433.8		16
72.29	odd	6		864.2.d.c.433.7		8
72.43	odd	6		216.2.d.c.109.1	✓	8
72.59	even	6		648.2.n.q.109.4		16
72.61	even	6		864.2.d.c.433.1		8
72.67	odd	6		648.2.n.q.109.5		16
144.11	even	12		6912.2.a.cj.1.4		4
144.29	odd	12		6912.2.a.cd.1.1		4
144.43	odd	12		6912.2.a.cj.1.1		4
144.61	even	12		6912.2.a.cd.1.4		4
144.83	even	12		6912.2.a.cc.1.1		4
144.101	odd	12		6912.2.a.ci.1.4		4
144.115	odd	12		6912.2.a.cc.1.4		4
144.133	even	12		6912.2.a.ci.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.d.c.109.1	✓	8	72.43	odd	6
216.2.d.c.109.2	yes	8	36.7	odd	6
216.2.d.c.109.7	yes	8	36.11	even	6
216.2.d.c.109.8	yes	8	72.11	even	6
648.2.n.q.109.2		16	36.23	even	6
648.2.n.q.109.4		16	72.59	even	6
648.2.n.q.109.5		16	72.67	odd	6
648.2.n.q.109.7		16	36.31	odd	6
648.2.n.q.541.2		16	24.11	even	2
648.2.n.q.541.4		16	12.11	even	2
648.2.n.q.541.5		16	4.3	odd	2
648.2.n.q.541.7		16	8.3	odd	2
864.2.d.c.433.1		8	72.61	even	6
864.2.d.c.433.2		8	9.2	odd	6
864.2.d.c.433.7		8	72.29	odd	6
864.2.d.c.433.8		8	9.7	even	3
2592.2.r.q.433.1		16	9.4	even	3	inner
2592.2.r.q.433.2		16	72.5	odd	6	inner
2592.2.r.q.433.7		16	9.5	odd	6	inner
2592.2.r.q.433.8		16	72.13	even	6	inner
2592.2.r.q.2161.1		16	8.5	even	2	inner
2592.2.r.q.2161.2		16	3.2	odd	2	inner
2592.2.r.q.2161.7		16	24.5	odd	2	inner
2592.2.r.q.2161.8		16	1.1	even	1	trivial
6912.2.a.cc.1.1		4	144.83	even	12
6912.2.a.cc.1.4		4	144.115	odd	12
6912.2.a.cd.1.1		4	144.29	odd	12
6912.2.a.cd.1.4		4	144.61	even	12
6912.2.a.ci.1.1		4	144.133	even	12
6912.2.a.ci.1.4		4	144.101	odd	12
6912.2.a.cj.1.1		4	144.43	odd	12
6912.2.a.cj.1.4		4	144.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.91009 - 1.68014i) q^{5} +(-1.32288 + 2.29129i) q^{7} +O(q^{10})\)	\(q+(2.91009 - 1.68014i) q^{5} +(-1.32288 + 2.29129i) q^{7} +(-1.87919 - 1.08495i) q^{11} +(4.02334 - 2.32288i) q^{13} -4.55066 q^{17} -6.29150i q^{19} +(-0.489766 - 0.848299i) q^{23} +(3.14575 - 5.44860i) q^{25} +(-3.75839 - 2.16991i) q^{29} +(1.00000 + 1.73205i) q^{31} +8.89047i q^{35} -1.35425i q^{37} +(-5.53019 - 9.57857i) q^{41} +(-2.85052 - 1.64575i) q^{43} +(5.04042 - 8.73027i) q^{47} +4.33981i q^{53} -7.29150 q^{55} +(9.76117 - 5.63561i) q^{59} +(1.67771 + 0.968627i) q^{61} +(7.80552 - 13.5196i) q^{65} +(2.59808 - 1.50000i) q^{67} +11.5830 q^{73} +(4.97188 - 2.87052i) q^{77} +(-4.32288 + 7.48744i) q^{79} +(2.06179 + 1.19038i) q^{83} +(-13.2428 + 7.64575i) q^{85} +4.55066 q^{89} +12.2915i q^{91} +(-10.5706 - 18.3088i) q^{95} +(-1.14575 + 1.98450i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 8 q^{25} + 16 q^{31} - 32 q^{55} + 16 q^{73} - 48 q^{79} + 24 q^{97}+O(q^{100}) \) 16 * q + 8 * q^25 + 16 * q^31 - 32 * q^55 + 16 * q^73 - 48 * q^79 + 24 * q^97

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